Questions in indefinite-integration

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$\int_{{}}^{{}}{\sqrt{1-\sin 2x}\ }dx=........,\ \ x\in (0,\ \pi /4)$
$\int_{{}}^{{}}{\frac{1+{{\cos }^{2}}x}{{{\sin }^{2}}x}dx}=$
$\int_{{}}^{{}}{{{\sin }^{-1}}}(\cos x)dx=$
$\int_{{}}^{{}}{\frac{dx}{\tan x+\cot x}}=$
$\int_{{}}^{{}}{({{e}^{a\log x}}+{{e}^{x\log a}})dx}=$
If $f'(x)={{x}^{2}}+5$ and $f(0)=-1$, then $f(x)=$
$\int_{{}}^{{}}{{{\tan }^{-1}}\sqrt{\frac{1-\cos 2x}{1+\cos 2x}}}\ dx=$
$\int_{{}}^{{}}{\frac{dx}{\sqrt{x}+\sqrt{x-2}}=}$
$\int_{{}}^{{}}{\frac{\sin x}{\sin (x-\alpha )}dx=}$
$\int_{{}}^{{}}{\frac{\cos x-1}{\cos x+1}\ dx=}$

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